I am working on an old comparator, and I have changed the light circuit to 12VAC to use an FDT halogen bulb. The bulb is 12V 100W, and I am using a 120V to 12V 150VA control transformer to power it. The bulb is burning out right around once a week. Can anyone give me an idea as to why? Any direction would be greatly appreciated!

As @cmartinez points out, a halogen bulb relies on high temp, thicker glass (usually quartz) with that cools slowly an some halogen gas in the tube - this allows the tungsten to re-deposit on the filament each time it is turned off. So, short cycling of a halogen bulb will kill (turning it off before the glass has time to warm up). Likewise, running it at low voltage so it never warms up will also kill it. Also, running it in an area with forced cooling if the bulb was designed for ambient will kill the bulb. To see if any of these three issues are shortening the life of the bulb, look for dark/black/gray deposits inside on the glass (tungsten vapor depositing on the glass instead of back onto the filament.

Running in small enclosures will kill it (Because it overheats or, if forced air cooling, it never reaches operating temperature).

@mcgyvr.. I've looked into it, and I can't find an LED that puts out 3000 lumens in such a small package.

@GopherT... I will make sure it doesn't get cycled without proper warm up. It is in a smaller space with not much air flow. The glass looks like it has a dark gray blotch of paint on it when it blows. It isn't just breaking the filament.

The sockets are responsible for getting rid of a significant amount of heat. Corrosion causes more heat at the contact point instead of less heat.
I would also mention that the power line voltage at my house is 250.1 VAC, rated 240VAC +/- 5%.
Putting a buck transformer in series with my 115V rated HPS lamps increased their lifespan from 2&1/2 years to, "I don't know". I've never burned one out in the 13 years since I bucked the power voltage down from 125 to 109 VAC.

I have transformers marked, "120/208/230"
I have water heater elements marked, "240 VAC".
I have a Fender Guitar amplifier with an accessory outlet marked, "115 volts".
My 1979 Clothes dryer had to be converted to a 120V rated Calrod heater instead of 115V rated coiled nichrome so the heater would last more than 3 weeks.
Engineering is always a series of compromises.
If you live in Gnaw Bone Kentucky, you have no reason to expect the same voltage as La Vegas.